I'm writing a merge sort function, but I get type error under such implementation:

mergesort :: (a -> a -> Ordering) -> [a] -> [a]
mergesort cmp xs = mergeAll (map (\x -> [x]) xs)
    where
      mergeAll :: [[a]] -> [a]
      mergeAll [x] = x
      mergeAll xs = mergeAll (mergePairs xs)

      mergePairs :: [[a]] -> [[a]]
      mergePairs (a:b:xs) = merge a b : mergePairs xs
      mergePairs xs = xs

      merge :: [a] -> [a] -> [a]
      merge as@(a:as') bs@(b:bs')
          | cmp a b == GT = b : merge as bs'
          | otherwise     = a : merge as' bs
      merge [] bs = bs
      merge as [] = as

And ghc says:

    Couldn't match type `a1' with `a'
      `a1' is a rigid type variable bound by
           the type signature for merge :: [a1] -> [a1] -> [a1]
           at /home/ice/Study/Haskell/tutorials/99Questions/21to30.hs:135:7
      `a' is a rigid type variable bound by
          the type signature for
            mergesort :: (a -> a -> Ordering) -> [a] -> [a]
          at /home/ice/Study/Haskell/tutorials/99Questions/21to30.hs:124:1
    In the first argument of `cmp', namely `a'
    In the first argument of `(==)', namely `cmp a b'
    In the expression: cmp a b == GT

But if I comment all type signatures, ghc works fine on it.
I would really appreciate it if you can point out what causes this question? And how
to fix it without changing the structure of the program (i.e. not adding function `cmp' as a parameter of `merge' etc.).
Thx.